This paper is motivated by a question whether it is possible to calculate a chaotic sequence efficiently, e.g., is it possible to get the $n$-th bit of a bit sequence generated by a chaotic map, such as $\beta$-expansion, tent map and logistic map in $o(n)$ time/space? This paper gives an affirmative answer to the question about the space complexity of a tent map. We prove that a tent code of $n$-bits with an initial condition uniformly at random is exactly generated in $O(\log^2 n)$ space in expectation.

翻译：本文源于一个关于能否高效计算混沌序列的问题，例如，能否在 $o(n)$ 时间/空间内获取由混沌映射（如 $\beta$ 展开、帐篷映射和逻辑斯蒂映射）生成的比特序列的第 $n$ 位？本文针对帐篷映射的空间复杂度问题给出了肯定回答。我们证明，在初始条件均匀随机的情况下，一个 $n$ 比特的帐篷码的期望生成空间复杂度恰好为 $O(\log^2 n)$。